Now, there’s some oddities in this graph. For one, the data starts at year 1957.5, presumably because each year’s value is actually a centered five-year average … which makes me nervous already, very nervous. Why not show the actual annual data? What are the averages hiding?

But what was of most interest to me are the error bars. To get the heat content figures, they are actually measuring the ocean temperature. Then they are converting that change in temperature into a change in heat content. So to understand the underlying measurements, I’ve converted the graph of the 0-2000 metre ocean heat content shown in Figure 1 back into units of temperature. Figure 2 shows that result.

Figure 2. Graph of ocean heat anomaly 0.-2000 metres from Figure 1, with the units converted to degrees Celsius. Note that the total change over the entire period is 0.09°C, which agrees with the total change reported in their paper.

Here’s the problem I have with this graph. It claims that we know the temperature of the top two kilometres (1.2 miles) of the ocean in 1955-60 with an error of plus or minus one and a half hundredths of a degree C …

It also claims that we currently know the temperature of the top 2 kilometers of the global ocean, which is some 673,423,330,000,000,000 tonnes (673 quadrillion tonnes) of water, with an error of plus or minus two thousandths of a degree C …

I’m sorry, but I’m not buying that. I don’t know how they are calculating their error bars, but that is just not possible. Ask any industrial process engineer. If you want to measure something as small as an Olympic-size swimming pool full of water to the nearest two thousandths of a degree C, you need a fistful of thermometers, one or two would be wildly inadequate for the job. And the top two kilometres of the global ocean is unimaginably huge, with as much volume as 260,700,000,000,000 Olympic-size swimming pools …

So I don’t know where they got their error numbers … but I’m going on record to say that they have greatly underestimated the errors in their calculations.

w.

PS—One final oddity. If the ocean heating is driven by increasing CO2 and increasing surface temperatures as the authors claim, why didn’t the oceans warm in the slightest from about 1978 to 1990, while CO2 was rising and the surface temperature was increasing?

PPS—Bonus question. Suppose we have an Olympic-sized swimming pool, and one perfectly accurate thermometer mounted in one location in the pool. Suppose we take one measurement per day. How long will we have to take daily measurements before we know the temperature of the entire pool full of water to the nearest two thousandths of a degree C?

PPS answer(s)
Outdoor pool: Never, each new day brings different ambient conditions.

Indoor pool in a tightly climate controlled environment: 500,000 days

So the oceans have warmed about 0.1C over the past 57 years but the Earth has warmed by 0.8C since 1979. Whats wrong with that picture, especially since the oceans cover 70% of the Earth’s surface and constitute 98+% of the heat sinking capacity. I don’t believe it.

PPPS: How much CO2 will be outgassed from the oceans based on the presumed 0.1C temperature increase of the oceans?

If the ocean heating is driven by increasing CO2 and increasing surface temperatures as the authors claim, why didn’t the oceans warm in the slightest from about 1978 to 1990, while CO2 was rising and the surface temperature was increasing?

This at least is possible and no contradiction. Ocean currents and therby connected heat transfer and overturn occurs on all timescales in the ocean. These variations may conceivably be due to heat moving in or out into/from deeper ocean layers.

Howver and regarding the ‘accurate measuring’ problem, a more viable method to determine (estimate) changes in in total ocean heat content would be through measuring sea level changes accurately. And this can be done at the surface, and with less probes (‘thermometers’) than in the swimming pool /the oceans, since gravity does not change over the time scales considered here.

Thermal heat expansion of ocean water is ~independent of water temperature, and thus changes in heat content and total volume match each other well. The contamination there is from melting land ice, and possibly a little from changing water content of cultivated land areas. Both these, however, should be easier to estimate/measure than 2000m ocean heat content using thermometers.

K Hutter added that politicians accused scientists of a high signal to noise ratio; scientists must make sure that they come up with stronger signals. The time-frame for science and politics is very different; politicians need instant information, but scientific results take a long time

And how many measuring devices were extant during this period that measured columns from 0 to 2000 meters and at what sampling frequency? Today our wide cast devices only meaure to 700 meters. So when and where did the other 1300 meters of measurement come from and at what percent coverage? To put it mildly, BULL HOCKEY! [ or.. water hockey (stick)]

Whether they are right or wrong I don’t think that they are claiming that. They are claiming to measure the average heat content over a five year period. (It is because they are taking the average that it makes more sense to think in terms of heat content that temperature.) Maybe their error bars are too small. But the error bars on an average will be smaller than the error bars on an individual measurement. An intuition that starts by thinking about a point measurement in a larger body or over a short period of time is unlikely to be correct. What is needed is analysis, not simple incredulity.

The numbers would appear to indicate the error lies in their estimate of ocean coverage

How did they achieve 100% data coverage at 700 meters starting in 1994? How did coverage at 2000 meters peak in 1994?

What exactly is their definition 100% coverage? Is it one reading per cubic meter per second, or one reading per cubic mile per year? Or is 100% coverage one reading per 1000 cubic miles per decade?

What is the volume of water measured and the number of readings over time, and how random is the sample?

If the measurements are taken from ships they are not at all random because shipping lanes are not random, they are determined by geography and weather patterns. There are large areas of the oceans where commercial shipping never travels, and other areas where shipping is highly concentrated.

PPS—Bonus question. Suppose we have an Olympic-sized swimming pool, and one perfectly accurate thermometer mounted in one location in the pool. Suppose we take one measurement per day. How long will we have to take daily measurements before we know the temperature of the entire pool full of water to the nearest two thousandths of a degree C?

Answer
You will never know the temperature of the pool to within two thousandths of a degree C. All you will know is the temperature at that particular spot, to within the accuracy of your thermometer. The pools that I have been in have warm and cold spots.

When Warmistas promulgate their cargo-cult ‘science’,
you’re supposed to genuflect and vote to outlaw carbon dioxide.
Error-finding critiques are only for ‘deniers’, not for Warmista Scripture.
When a Warmista claims accuracy of 1 part per trillion, then accept it!
Have faith in science and shut up! Don’t scrutinize, don’t doubt, don’t even look!

G. Karst says:
April 23, 2012 at 7:30 am
I am 52.31847295482937529573648254482% confident in the results. GK
============================================
And it’s a well-established fact that 76.38% of all statistics are made up on the spot

Thank you for your analysis – I’m going to show this to my teenage daughters as an example of how what some scientists present as “settled science” can be demolished in several paragraphs by other scientists; ie in minefields we cannot afford to passively “be informed” but must consider different views.

Willis, I agree completely; having spent 15 years with a Fortune 50 Aerospace company as the senior process/quality engineer for the division, and also as a past Chairman of the American Society for Quality. You’ve just encapsulated everything I see wrong about the entire AGW meme. Thank you. :)

Leif provides a link to the paper (Thanks!), that includes this scarey bit”

“If this heat were instantly transferred to the lower 10 km of the global atmosphere it would result in a volume mean warming of this atmospheric layer by approximately 36°C (65° F).”

Then they admit this can’t and won’t happen. I wonder whose idea it was to make this calculation and why? Why not calculate how many vaporized climate scientists can dance on the head of a pin? Equally useful.

From a process engineering standpoint, it is impossible to get such high precision.

I work at a bakery, where we make about a million lbs of bread each week (seasonally averaged). We have a machine called a proof box. It is a room with about the same internal volume as an olympic sized swimming pool. The bread moves through this room on a continuous conveyor line. We have both wet and dry bulb thermometers placed throughout the interior, and we run a device called a mole through periodically to callibrate our climate controls. The climate controls inside our proof box are state of the art. There is a direct connection between our ability to control that environment precicely and our quality/profitability. Bread that doesn’t rise properly ends up going in the pig feed trailer. When money is at stake, you can bet your left leg that every effort is made to get it right. I can tell you that in a fluid such as air or water, convection can lead to very uneven temperature profiles. The temperature you read at any given location may be totally unrepresentitive of the temperature just a few feet away, and no given set of temperature/humidity readings can ever be assumed to be representative of the area as a whole. We have seen faulty trends of increase and/or decrease many times due to the quirky ways air can circulate inside the box and/or problems with the instruments.

As an added note: Taking two readings seperated by some space and assuming that the area between them has a value averaged between the two measurements is insane.

This is the same game as the precision and accuracy problem we all face when we try to treat a dynamic, heterogeneous, gross, and I mean Gross, amount, volume in this case, as if the work was being done in a laboratory. Nonsense is not a strong enough term. We can’t even achieve this in relatively static volumes such as large rock masses (hundreds of cubic meters not millions of cubic kilometers.) Who knows maybe they believe in the tooth fairy too. More seriously I have written a number of essays trying to address the precision/accuracy business from a practical and philosophical point of view. It is another one of those seemingly simple things that turns out to be highly complex.

“If the ocean heating is driven by increasing CO2 and increasing surface temperatures as the authors claim, why didn’t the oceans warm in the slightest from about 1978 to 1990, while CO2 was rising and the surface temperature was increasing?”

Maybe because CO2 has nothing to do with Ocean heating.

“The solar radiation penetrates the ocean to 100 metres at visible wavelengths but to much shallower depth as wavelength increases. Back radiation in the far infra-red from the Greenhouse Effect occurs at wavelengths centred around 10 micrometres and CANNOT penetrate the ocean beyond the surface ‘skin’.”

It is good to see the paper. It is good to read the serious questions. Nothing surprises me more than all the ocean heat content claims. The oceans are not only huge, but have only an average temperature of about 4°C.

In your critique, you overlook a fatal flaw in the argument of Levitus et al. This is that they.mislead their readers by implying that their data contain far more information than is present in them. They accomplish this feat by a method of presentation that dupes readers into vastly overcounting the empirical basis for their conclusions.

If you are correct, Levitus et al. average the data over 5 years. However, it is a 30 year averaging period that is canonical in climatology,. It follows from a 30 year averaging period that there are either 0 or 1 statistically independent values in the interval between 1957.5 and 2010; that’s far too few values for generalizations to be made about the cause of fluctuations in the heat content. Generalizations cannot be made but it seems to the statistically naive reader as though generalizations can be made.

Even the draft paper at NOAA states a similar order of magnitude in temperature … which is silly as it is impossible in practice to achieve measurements of such precision across multiple sets of instruments operating over long periods in uncontrolled environments.

Never believed that anyone can measure anything to any real sense to a thousanths of the degree C, rates of rise in temperature or actual rises in atmospheric or oceanic media. Phil Jones was always keen to show rates of atmopsheric warming to a thousanths of a degree which frankly strikes me as very unlikely to be achievable! I am alway open to persuasion!

“………And stop insulting the work of other scientists Willis – Climategate Email 4693.txt teaches us:-
Maybe it is an illusion or prejudice on my part, but somehow I am not convinced that the “truth” is always worth reaching if it is at the cost of damaged personal relationships….”
********************
I beg to differ:

If the “lie” is part of a monumental hoax that will destroy the future of my children, then I believe coming to the “truth” IS worth a damaged personal relationship.

When perpetuating a “lie” causes the destruction of serious, honest, REAL scientists, then finding the “truth” IS worth a damaged personal relationship.

I believe that there is a different lesson in your quote: (Not necessarily in the context of this one report, but as part of the broader CAGW mime) When self-proclaimed “scientists” are destructively wrong using fraudulent data and McCarthy-ite tactics, then a failure to act is, at best, negligence, at worst, cowardice.

The way these guys make up statistics is chilling, and even more chilling is the way most gullible people believe them. Common sense contradicts many of the ‘statistics’ climate activists come up with. Help get the truth out by visiting ClimateTruthIreland.

It is frequently possible to measure changes more accurately than absolute values.

…unless you are measuring those changes with 3000 diving, drifting robot buoys, in an environment which changes every minute, and every day, and cycles through 4 seasons every year, and each year on a day by day basis has never, ever been the same as any other year, and no consecutive sets of measurements are ever taken in exactly the same place or under the same conditions….

What you need to get increasing accuracy with repeated measures is, strangely enough, repeatable conditions.

@Rich Lambert
The reason why climate science will not agree to adhere to ISO standards (there are many different standards depending on the industry) is because that would involve a ground up systems audit of all the processes, measurements etc. thereby exposing their work to scrutiny outside their control. We mustn’t have that. My company gets audited 4x per year.

If there are any fellow Metrologists following, do you also split a gut laughing when seeing the claimed error bars for many of these so-called “studies”? In the real world, uncertainty must be accounted for empirically, not by playing statistics games.

I don’t know whats the matter with you. You’ll be claiming next that we don’t know the Global SST back to 1850 to fractions of a degree, or that tree rings can’t tell us about the global temperature a thousand years ago to fractions of a degree. :)

Its much easier to accurately measure volume than than temperature. Yet over the period considered by this study, estimates of ocean volume have been reduced by around 10 million cubic kilometres or 5 Gulfs of Mexico, or 1% of the total. Maybe the ‘missing heat’ was in that disappearing water? (http://www.tos.org/oceanography/archive/23-2_charette.pdf)

PPS—Bonus question. Suppose we have an Olympic-sized swimming pool, and one perfectly accurate thermometer mounted in one location in the pool. Suppose we take one measurement per day. How long will we have to take daily measurements before we know the temperature of the entire pool full of water to the nearest two thousandths of a degree C?

Answer
You will never know the temperature of the pool to within two thousandths of a degree C. All you will know is the temperature at that particular spot, to within the accuracy of your thermometer. The pools that I have been in have warm and cold spots.

I have never understood the point of plotting these graphs (Figure 1) with a Y axis expressed in heat content (even heat content anomaly). What does it mean to have a value of -4 or +8 x 10^22 J? Do they truly mean to imply that the heat content ranges 100 fold? (0.1 to 10 x 10^22 J)?

Willis, your temperature plot makes more sense to me. And it’s interesting to contemplate that a 100x change in heat content can result in an imperceptible change (0.01°C) in temperature, illustrating once more how inconceivably enormous the ocean heat sink really is.

Specious accuracy and woefully inadequate precision are endemic in this field.

Hard to see how this protocol results in an estimate that has any bearing on the real values:

“From every observed one-degree mean temperature value at every standard depth level we subtract off a climatological value. For this purpose we use the monthly climatological fields of temperature from Locarnini et a. [2010]. Then we composite all anomaly values in each one-degree square by five-year running compositing periods. Next the same objective analysis procedure used by Locarnini et al. [2010] is applied to these gridded, composited anomaly values and a global, gridded field with temperature anomaly values defined in every one-degree square is produced for each standard depth level. To compute heat content at each gridpoint the specific heat and density were computed using annual climatological values of temperature and salinity from Locarnini et al. [2010] and Antonov et al. [ 2010].” –Levitus et al. (2012)

Whether they are right or wrong I don’t think that they are claiming that. They are claiming to measure the average heat content over a five year period. (It is because they are taking the average that it makes more sense to think in terms of heat content that temperature.) Maybe their error bars are too small. But the error bars on an average will be smaller than the error bars on an individual measurement. An intuition that starts by thinking about a point measurement in a larger body or over a short period of time is unlikely to be correct. What is needed is analysis, not simple incredulity.

Thanks, JK. So if someone says they just met a man who is 27 feet (8 metres) tall, and I say I don’t believe that in the slightest, your response would be “what is needed is analysis, not simple incredulity”?

Sometimes incredulity is sufficient … but if you want analysis, see my post “Decimals of Precision” cited up top.

Willis, I agree completely; having spent 15 years with a Fortune 50 Aerospace company as the senior process/quality engineer for the division, and also as a past Chairman of the American Society for Quality. You’ve just encapsulated everything I see wrong about the entire AGW meme. Thank you. :)

My thanks to you, George. Give me an engineer over a scientist any day, they tend to have actual real-world hands-on experience with the issues under discussion. Any other process engineers out there are welcome to give us your professional opinion as well.

From a process engineering standpoint, it is impossible to get such high precision.

I work at a bakery, where we make about a million lbs of bread each week (seasonally averaged). We have a machine called a proof box. It is a room with about the same internal volume as an olympic sized swimming pool. The bread moves through this room on a continuous conveyor line. We have both wet and dry bulb thermometers placed throughout the interior, and we run a device called a mole through periodically to callibrate our climate controls. The climate controls inside our proof box are state of the art. There is a direct connection between our ability to control that environment precicely and our quality/profitability. Bread that doesn’t rise properly ends up going in the pig feed trailer. When money is at stake, you can bet your left leg that every effort is made to get it right. I can tell you that in a fluid such as air or water, convection can lead to very uneven temperature profiles. The temperature you read at any given location may be totally unrepresentitive of the temperature just a few feet away, and no given set of temperature/humidity readings can ever be assumed to be representative of the area as a whole. We have seen faulty trends of increase and/or decrease many times due to the quirky ways air can circulate inside the box and/or problems with the instruments.

As an added note: Taking two readings seperated by some space and assuming that the area between them has a value averaged between the two measurements is insane.

John Endicott says:
April 23, 2012 at 9:07 am
Mark says:
And it’s a well-established fact that 76.38% of all statistics are made up on the spot
============================================

That was the old studies, newer, more accurate, studies put it at 82.3459% +-0.002% :)
———————-
The increase is because they are now including climate science in the statistics.
Old numbers were pre CAGW.

PPS—Bonus question. Suppose we have an Olympic-sized swimming pool, and one perfectly accurate thermometer mounted in one location in the pool. Suppose we take one measurement per day. How long will we have to take daily measurements before we know the temperature of the entire pool full of water to the nearest two thousandths of a degree C?

Answer
You will never know the temperature of the pool to within two thousandths of a degree C. All you will know is the temperature at that particular spot, to within the accuracy of your thermometer. The pools that I have been in have warm and cold spots.

And to make matters worse, in any pool of water exposed to the suns radiation you will always have temperature differentials in any given volume of water, where one area is slightly warmer or colder than another area. I own a pool service and spa repair business. When I add a colored chemical to the water, I love to watch he the chemical disperses. On a nice warm sunny day, you can see the chemical dye shifting this way and that as they disperse in the water, carried along by currents created by slight temperature differences in different areas of the pool of water.

Give a million monkeys each a rectal thermometer and you’d be surprised what you can measure, as any primatologist will tell you. For the heat reported–however accurately or not–I get a sea level rise of 14mm in 50 years, without acceleration but clearly dangerous (quick, raise the dikes!). This is better explained as recuperation from the LIA than anything else. –AGF

Many in the solar terrestrial physics community seem totally convinced that solar output changes can explain most of the observed changes we are seeing … the solar terrestrial group are not going to go away

Rich Lambert says:
April 23, 2012 at 7:44 am
“Climate science needs something like the ISO 9000 quality control standards used by industry.

REPLY: Yep, I argued for this back in 2008:”

They need a disciplinary body created by a legislative act as is the case for professional engineers. They have this for engineers because when they are wrong, bridges can fall down, mines collapse, dams breach, buildings fall over…. We have reached a point where incompetence and advocacy in science is heading for doing real damage to civilization and risk of death for billions by taking away abundant, affordable energy and wasting scarce resources and wealth on unworkable alternatives. A few of the main scientist advocates, well known to all, would already have been barred from practicing their “professions” by now.

Apparently, Levitus felt under pressure to not to produce lower trends since that would be even less consistent with AOGCM simulations. The errors really are gross – the trend line in the global heat content graph disagrees to the data in the table by approaching 25%, if I recall correctly.

Even worse, when James Annan reported the errors to the editor at Science, he refused to anything about the matter.

Given this history, I find it impossible to assign a high level of confidence to any study authored by Levitus.

If they really believe they can make measurements at that accuracy I submit that they should be willing to wager a months salary that in a blind test two teams of their choice, measuring the oceans temperature on the opposite side of the same boat at the same time and depth can get measurements that agree with in 2x their alleged accuracy.

They will use new temperature measuring devices of their specification supplied directly from the manufacture.
Each team can make any number of measurements within a one hour time period.
All measurements must be made at the same depth. They will report their measurements in real time to an independent 3rd party as they take them, for offical documentation of the readings.
Then apply their pre-documented processing to that officially certified data converge on what they assert is the true temperature of the ocean at that location at that time.
They teams will at no time be aware of or able to determine the temperatures being reported by their opposite team.
The final measurements of the two teams must agree to an accuracy of 4 thousandths of a degree C.

If they win they get to keep their previous months salary. If they lose, all the team members donate a months salary to the charity of Anthony’s choice.

Refresh my memory on simple error bars, please. If I measure that an object moved 2.00 meters in 4.00 seconds, and my meter stick is in cm and my stopwatch in hundredths of a second, my error bars would be “it moved 2.00 m +/- 0.005 m in 4.00 s +/- 0.005 s”, correct?

Now if I use those numbers to determine velocity I would get 0.50 m / s +/- 0.005m/0.005s?

This is what happens when your physics classes were [cough] decades ago…

Climate science needs something like the ISO 9000 quality control standards used by industry.
_________________________
NO THANK YOU!

I used to believe that too until the FDA’s HACCP Requirements. ISO (and HACCP) substitute paperwork for actual testing and depends on faith in others who have a vested interest in lying.

This is what Quality Engineers like me think. (Quality Magazine)

“…Scott Dalgleish, [is] vice president of manufacturing at Spectra Logic Corp., a Boulder, CO, maker of robotic computer tape backup systems. Dalgleish, an ASQ certified quality manager who has worked in the quality profession since the late 1980s, is not happy with the direction that the quality movement has taken in recent years. And he sees the ISO 9000 family of standards as the primary negative influence.

Among other things, Dalgleish contends that ISO 9000 misdirects resources to an overabundance of paperwork that does almost nothing to make products better, while fostering complacency among top management and quality professionals alike. The recent conversion to the 2000 version of the standard has only made things worse, he says. While ISO 9000:2000 has almost no effect on how good companies operate, it requires huge amounts of time for document revision that could better be spent on real quality improvement, he believes.

I’m wondering if there might be a silent majority of Quality readers out there on the topic of ISO 9000. The response to my July editorial, “Eliminate ISO 9000?,” was the heaviest that we have received in some time. I got lots of e-mails from readers about the piece, which reported the views of Scott Dalgleish, a quality professional who has been publicly critical of the impact of ISO 9000 on manufacturers, and has suggested that companies eliminate ISO 9000 altogether from their quality management systems.

Many of the responses were quite articulate, and some were humorous and entertaining. You can read a sampling in this month’s Quality Mailbag department on p. 12.

One thing that struck me about the letters I received is that almost all expressed some level of agreement with Dalgleish, particularly on issues related to excessive ISO 9000 documentation requirements. As you’ll see in the Mailbag department, one reader even said that his company has already dropped its ISO 9001 certification with no apparent negative effects.What surprised me is that the July editorial elicited no ardent rebuttals in defense of ISO 9000.

No amount of paperwork can substitute for honesty. A good documentation system is always useful but it should not be the area of focus. Decent honest testing and data gathering is the backbone of all science including Quality Engineering.

Check out the central limit theorem to find out what they’ll invoke for their spurious precision. If you’ll divide the precision of one instrument with the square root of the number of the measurements, you’ll find out how they obtained those error bars. So basically they decreased the size of the error bars over time by either increasing the number of measurements, or by increasing the instrument’s precision. The problem is… they apply the central limit theorem in a pseudo-scientific way. It is proven for independent variables (the classical one requires also to be identically distributed, which does not happen for temperatures on different points of Earth, very easy to verify that experimentally, both the median and expected values vary – this condition is weakened in variants, but the theorem does not hold for ANY condition).
The problem is… temperatures are not really independent. There is a dependence both in space, and in time.
That is, temperature in a point is dependent on the temperatures nearby, and the temperature at time t is dependent on the temperature at a previous moment (both the local one, and the nearby ones). That’s why one can have something like heat equation in physics. Because the temperatures are not independent.
So, it’s a pseudoscientific way to apply the central limit theorem when it does not apply. Unless they have a proof for it to hold even if variables are dependent. I don’t think they ever presented such a proof.

Let me try again. This is not intended as an actual error analysis. The paper has not been officially published yet, so the appendix containing the author’s own analysis is not yet available. We should wait until that analysis is available before discussing it.

However, to get an idea of the power of averaging suppose that there are 3000 argo floats, each reporting once every 10 days for 5 years. This will give 547,500 measurements. Each of those measurements will have an error associated with it. But to the extent that the error is random these will cancel out. From basic statistics we can expect that the error on the mean will be down by a factor of about square root of 547,500 which is about 740. That means that if there is a random error in each individual float of about 1.5 degrees the error on the 5 year global mean will be about 0.002 degrees.

What would this apply to? Well each Argo measurement has to represent a large volume of ocean. Some float will find themselves warmer than the region they need to represent and some will find themselves cooler. If those differences are random, then in the average they will, to an extent, cancel out. Similarly, some thermometers will read a bit warm and some a bit cool. Of course it may be that all floats are biased warm or cool. That wouldn’t matter for assessing changes. It would matter if there was a systematic change in the bias. That would certainly require additional analysis.

Certainly it is right that trying to make a single measurement to 0.002 degrees is absurd. But is trying to make an Argo measurement to 1.5 degrees plausible? I don’t know. Here’s the thing: I don’t believe that anyone here knows off the top of their head either, or could figure it out with a few minutes thought about some analogous experience. I’m not arrogantly dismissing anyone as stupid. I am sure that we could all figure out a reasonable estimate if we put the work in. Of course I would like to see how the authors justify their estimate. But I don’t think that the answer is obvious.

You still might ask why a five year average is legitimate? Willis hints at this question. But we could chose any time period. The error on the one year averages will be higher. But what is special about one year? The one month, one week, and one day averages could be calculated with greater and greater error. The ten year average could be calculated with smaller error.

Presumably the authors would be interested in the highest frequency information they can get, and presumably chose a 5 year period in part as a compromise between error and time resolution.

In a case like this averaging works by sacrificing some information (for example year to year variation) in order to gain precision in another measure, the mean. It seems to me that, at least in general terms, this is an essential use of statistics throughout science. Maybe it has been applied badly here. But even if it has I don’t see any evidence presented that averaging is a fundamentally wrong strategy in this case.

To be clear, I quite agree with this statement:

“If you want to measure something as small as an Olympic-size swimming pool full of water to the nearest two thousandths of a degree C, you need a fistful of thermometers, one or two would be wildly inadequate for the job. And the top two kilometres of the global ocean is unimaginably huge, with as much volume as 260,700,000,000,000 Olympic-size swimming pools …”

I also agree that temperature measured by each Argo float will have a much, much larger than error than 0.002 degrees when taken as measure of surrounding ocean. That is not what I’m disputing.

I won’t defend the author’s error bar of 0.002 degrees, as I have not seen their justification. But I just don’t see any evidence presented in this post that it is possible to measure the global mean with much greater accuracy than that.

PS Having written this I have just read Willis’ previous post on Decimals of Precision where I see he addresses my argument above with the point that by this logic 30, or even 3, buoys could do a passable job. But square root scaling is just a back of the envelope estimate and to answer that I think we need to delve into details. For example, it may be that a large number of buoys is needed for spatial coverage, but we could do a passable with one hundredth of the number of observations from each buoy.

But at that point I think that it makes more sense to go from temperature to heat content and consider other details anyway.

Gary Pearse says:
April 23, 2012 at 11:22 am
They need a disciplinary body created by a legislative act as is the case for professional engineers. They have this for engineers because when they are wrong, bridges can fall down, mines collapse, dams breach, buildings fall over…. We have reached a point where incompetence and advocacy in science is heading for doing real damage to civilization and risk of death for billions by taking away abundant, affordable energy and wasting scarce resources and wealth on unworkable alternatives. A few of the main scientist advocates, well known to all, would already have been barred from practicing their “professions” by now.
___________________________________
That I can certainly agree with. I took the ASQ Quality Engineering tests to be come certified although that is not the same as a PE. Giving engineers/scientists LEGAL immunity when the company is cheating is also a big plus that comes with being a PE.

Just one more comment about that: one does not measure errors (so not those are the random variables the theorem is all about), but measures temperatures (those are the random variables that the theorem would be about, if they would be independent… the problem is, they are not).

Small world! :) I knew Scott thru ASQ. He’s not the only one who had problems with the ISO concept, and related auditing industry. It was a godsend for consultant larvae. What isn’t often mentioned is that the ISO auditors or their parent organization are not contractually liable for anything. That remains with the audited company. So there is really no incentive for a company to contract with an auditing organization, such as ASME or any of the many others, especially since the costs of doing so are significant. Then there was that loophole – self-certification. And of course various regulatory agencies get very nervous about it. FAA in my case.

We had this discussion at Boeing in the ’90’s. If you go back in the history of the 9000 series you’ll find that it’s primary raison d’etra was to ease trade restrictions and such within the budding European Union, by imposing standards of various sorts on the participating countries. It was sold to US companies as a way to ease entry into Euro markets.

I’m a little surprised that it’s still around, actually. Anything a company needs to know for QA/process control is available in many books on the subject from Juran, Deming, etc. as well as professional’s like Scott.

Rich Lambert says:
April 23, 2012 at 7:44 am
Climate science needs something like the ISO 9000 quality control standards used by industry.

REPLY: Yep, I argued for this back in 2008:

I’ve said the same thing here before too. I never believed that peer review was adequate quality assurance and neither do many regulators (e.g. the USFDA, USNRC). Actually better would be something less custormer focused, more along the lines of ISO 13485 or 21CRF820, Good Manufacturing Practices, which require you to fire the customer if they cut corners, are known to be engaging in fraud or dangerous practices.

“Sorry NSF, I’m returning your cheque because the Administration is misusing and misrepresenting my research to the National detriment”

Kelvin Vaughan says:
April 23, 2012 at 8:52 am
Why don’t heated swimming pool owners pump carbon dioxide into their pools. They will need less heating then?
————————
My guess is it would take a whole lot of CO2 to keep it warm in the winter.
/sarc

At the risk of not preserving anonymity, I know the company that makes the sensors on the ARGO floats – competitors of ours….

It is perfectly reasonable that they claim an accuracy of better than ±0.002°C for any individual measurement. In fact this particular company has an excellent reputation and can achieve even better than that. In order to achieve this claimed accuracy, they do pretty much what we do – basically you calibrate your sensors in a highly controlled environment, against highly accurate standards. Amongst other things, this means regular checking of your reference sensors against Triple Point of Water cells, Melting Point of Gallium cells, etc. It also means your calibration laboratory is temperature controlled (much like Gary Swift’s proving oven, above), and uses well stirred, insulated and very stable liquid baths. All of which is as you might expect.

Being in possession of several such insulated and stable liquid baths, I can tell you that the pinnacle of stability that we can achieve in a highly controlled calibration environment is to be able to hold ~1m³ water to ±0.001°C for about a minute or so* (what I mean by that is that taking point measurements at say 1Hz intervals in an agressively stirred bath, the peak to peak noise over a minute will be less than ±0.001°C). Over a day it may fluctuate by up to ±0.05° , or perhaps more if we are not careful. We can hold smaller volumes (1 or 2 litres) to perhaps ±0.0005°C for 2 or 3 minutes on a good day*. Not having been given a guided tour of our competitor’s facility I am straying into guesswork, but I would imagine that this is similar to their own experience.

My eventual point is that I agree with you, Willis. We can and do try our hardest to measure to this level of accuracy for a single measurement, but to suggest that an entire dataset can be reduced to a single value with this same level of accuracy just doesn’t add up. It fails the smell test. We go to a hell of a lot of effort to be able to measure temperature to this precision and accuracy in a controlled environment. The sea is not a controlled environment – I see data all the time where people take a temperature profile at a site, and then take another a few minutes later, and the results have changed by fractions of a degree (if they are lucky – sometimes it’s completely different). Even within a single profile, at “stable” conditions, the temperature data will vary within a metre or two by more than a couple of millidegrees.

I put my hands up – I am not a professional statistician, but am obviously familiar with most simple principles such as averaging to reduce white noise, statistical significance, distributions, SD , etc, etc; I am however a scientist of a certain stripe by (first degree) training, and now a bit-part engineer, production engineer, finance guy, salesman and HR “expert”, as most entrepreneurs end up being, with an added dose of expertise in one’s chosen field, which in my case happens to be oceanography. The oceans are a highly dynamic environment, not a controlled one. I could be persuaded that minute by minute readings of a single location over a year could yield an average for that exact location to this order of millidegree accuracy. Would that average mean much? Not in isolation, no. I just don’t find it conceivable that the sporadic nature of ARGO measurements (and highly sporadic methods beforehand) can yield that level of accuracy for the whole globe. A finger in the air (or dipped in the sea)? I would suggest that considering their paucity of data, combined with the variability of the environment they are operating in, it would not be unreasonable to think that the globalised average number (over the top bit of the ocean only) was correct to within ±2°C , whatever that single distilled number is actually worth. But what do I know? Two things:

1) When the guys who make your test equipment** doubt your conclusions, there is something seriously wrong.
2) There should be many many more sensors in the sea ;)

(*) As measured against many 10’s of thousands of dollars worth of measurement bridges and PRTs.
(**) Just to reiterate – my company doesn’t make ARGO sensors, just instruments with similar sensors.

Let me try again. This is not intended as an actual error analysis. The paper has not been officially published yet, so the appendix containing the author’s own analysis is not yet available. We should wait until that analysis is available before discussing it.

If the world media weren’t already discussing it I’d agree with you. Since they are, I wanted to take a preliminary look. I freely admit above that this is not an actual analysis. I, like you, am waiting to see how they’ve justified those tiny errors. I’m gambling here with my statement that the error bars are underestimated.

However, to get an idea of the power of averaging suppose that there are 3000 argo floats, each reporting once every 10 days for 5 years. This will give 547,500 measurements. Each of those measurements will have an error associated with it. But to the extent that the error is random these will cancel out. From basic statistics we can expect that the error on the mean will be down by a factor of about square root of 547,500 which is about 740. That means that if there is a random error in each individual float of about 1.5 degrees the error on the 5 year global mean will be about 0.002 degrees.

Thanks, JK. You are correct in general. There are, as always, two questions. One is whether their assumption of random errors is correct. The other is whether they have done all parts of the statistics correctly. I am engaged in some fascinating research on that question right now, more to follow.

PS Having written this I have just read Willis’ previous post on Decimals of Precision where I see he addresses my argument above with the point that by this logic 30, or even 3, buoys could do a passable job. But square root scaling is just a back of the envelope estimate and to answer that I think we need to delve into details.

Say what? Square root scaling is not just “back of the envelope”, it is built into the mathematics of how we calculate errors. You depend on it and call it “basic statistics” in your example above. I agree, however, that to answer the question we need to delve into the details.

For example, it may be that a large number of buoys is needed for spatial coverage, but we could do a passable with one hundredth of the number of observations from each buoy.

That’s not true, because the number of observations per buoy drops out of the equation. If you get accuracy Z from X buoys each taking Y observations per year, if you have ten times the buoys you get an extra decimal of precision regardless of whether Y is 10 or 1000 observations per year (as long as Y is constant).

Just a comment on standardization in general: There are 3 basic types of standardization. In Europe and some other countries, Standards carry the weight of law and are enforceable as such. In the US we have a voluntary Standards system, which is usually contractually enforced between companies and their customers, but only carries civil liability in most cases. In Asia, Standards are usually company based – or in the case of Japan within the Kiretsu (sp?) – a large company will have their own internal standards that are imposed on suppliers. Very little government involvement.

These different systems often result in trade problems with import/export, as we see from time to time, with regard to products and commodities.

A bit of trivia – the ancient Chinese dynasties were among the first to implement quality and process control standards. A bow and arrow from one manufacturer would be indentical to that from another, or somebody would lose their head. Same goes for many other ancient cultures. The Pyramids in Egypt could not have been built without formal standards (of measurement, process, etc.) that were rigidly enforced.

“That’s not true, because the number of observations per buoy drops out of the equation. If you get accuracy Z from X buoys each taking Y observations per year, if you have ten times the buoys you get an extra decimal of precision regardless of whether Y is 10 or 1000 observations per year (as long as Y is constant).”

Forget the ocean data. I don’t buy that we have 1/10th of enough thermometers to measure the air temperature. When the temperature varies by as much as 10F on my way to work(15 miles) outside Denver and the closest NOAA station is in CO Springs, there is not enough data to plot global temperature. And don’t get me started on all the corrections they make.

There has been a lot of discussion about statistal inference of the claimed accuracy of the measuring of ocean heat, reverse engineered from temperature change. I side with Willis on his take of things here. He is doing an excellent job.

However, one important thing that needs to be stated here is that the measurements ( regardless of the claim of accuracy ) do not demonstrate that there has been any change in the Greenhouse factor G, which is the difference in the spectrally integrated outgoing long wave radiation compared to the surface blackbody emission, or G = Sg – OLR. That is what really counts, and measuring the ocean heat content does not identify what specific wavelengths of energy contributed to warming, regardless of the accuracy of the amount.. There is no way to separate the contributing wavelengths that vary anywhere from solar ultra violet to the far end of the infrared spectrum, so in this regard, the claim of a rising heat content as being a proof that greenhouse gases were the cause is patently ridiculous.

A regular thermometer is fundamentally a point-source measurement.
That is: The actual instrument is only competent at measuring the temperature of the material at ‘one point’ – the tip of the thermometer.

None of the satellite methods are point-source measurements. They have different issues – but they’re -fundamentally- integrating in their operation.

Is there any evidence of 1955 marine thermometer temperature measurement having a measurement accuracy better than +/- 0.5 degrees ?
**********************************************************************************************

reclaimreality says:
“Thermal heat expansion of ocean water is ~independent of water temperature, and thus changes in heat content and total volume match each other well.”

Huh? Ever looked up the coefficient of expansion for water? It varies highly with temperature and drops to zero as the temperature drops down to zero at about 4 degrees C. So that presents a challenge (and a benefit) in that heat entering the cold, deep layers of the ocean has little impact on sea level!

“Square root scaling is not just “back of the envelope”, it is built into the mathematics of how we calculate errors. You depend on it and call it “basic statistics” in your example above. … the number of observations per buoy drops out of the equation.”

I don’t think it’s quite as simple as that. Possibly what you say is true for large numbers of observations well enough spaced in space and time.

Consider your PPS problem. As has been said, however many measurements you take at one point – even millions – will not give you a good average for the pool temperature.

However, if you are allowed to take the same number of measurements at random positions then your measurements will eventually converge on the average (presuming that the average is constant in time).

I think those are different statistical problems, which show that it is not simply a question of the number of measurements.

For an analogous situation with the planet suppose that you were allowed to take as many million observations as you like, but were restricted to one hemisphere.

Or suppose that you could take as many observations as you like but they were restricted to a few time points across 5 years.

Coverage matters, which is why it’s hard to do the job with three buoys and many measurements (also you may land up taking so many measurements from each buoy that correlation between measurements starts to matter much more, so after a certain point they are not really independent.)

I guess that there are contributions to the error which are large for small numbers of buoys, reflecting the problem of limited coverage, but go to zero for better coverage. With large numbers and good coverage error will be more square-root like, but there may be other complications, too.

It is easy by ‘intuition’ to say that 3 or 30 buoys is too few, and that millions would be adequate. That’s like the case of the 28 foot man don’t think it’s a co-incidence that the number of buoys we have is in the middle of this range. Most likely it was designed at minimum cost to get a worthwhile answer. That means, if the designers have done their job, that the error will likely be on the edge between obviously excellent and obviously terrible.

I have just scanned the version the Bob linked above that has the error calculations. This details the error propagation involved in their gridding method based on the variance of the readings. Unless I have misread it, it makes NO reference to the measurement uncertainty, ie it assumes (implicitly) that the measurement uncertainty is zero.

JK: However, to get an idea of the power of averaging suppose that there are 3000 argo floats, each reporting once every 10 days for 5 years. This will give 547,500 measurements. Each of those measurements will have an error associated with it. But to the extent that the error is random these will cancel out. From basic statistics we can expect that the error on the mean will be down by a factor of about square root of 547,500 which is about 740. That means that if there is a random error in each individual float of about 1.5 degrees the error on the 5 year global mean will be about 0.002 degrees.

Willis:
>>
Thanks, JK. You are correct in general. There are, as always, two questions. One is whether their assumption of random errors is correct. The other is whether they have done all parts of the statistics correctly. I am engaged in some fascinating research on that question right now, more to follow.
>>

No.This is the fundamental fallacy behind the ridiculously low ARGO uncertainty. You do not have 547,500 measurements of the same thing , that would allow the ‘divide by square root’ thing. You have 547,500 separate measurements of separate temperatures each with the full uncertainty. An uncertainty that is far larger than the simple platinum sensor precision.

Some part of that uncertainty , the instrument calibration uncertainty, will be reduced in this way over the thousands of individual floats. In any case it will probably be negligible compared to other errors.

However, that idea can not be applied to averaging of the temperatures which introduces a whole realm of other uncertainties. Principally, how representative is one reading at one point and a depth of the average temperature of the HUGE volume of water that it is being taken to represent. The uncertainty here is not millikelvin , it’s probably several degrees. That is several orders of magnitude bigger than some silly claims based on the total number of individual measurements as JK suggested above.

This representative accuracy of the one temperature then has to be added to the variance of the individual readings used to calculate the propagation errors in the paper.

Just how that will affect the overall uncertainty needs digging into but it will make a significant difference.

The problem here is that this has been totally ignored without the slightest discussion or recognition in the paper. Once again, climate scientists seem quite incapable (or unwilling) to correctly asses the uncertainty in their work.

Climate science needs something like the ISO 9000 quality control standards used by industry.”
Not a bloody chance! These clowns are all ready spewing out enough useless paperwork(and killing millions of innocent trees).All ISO 9000 and others do is produce jobs for writers and guys in companies like KPMG. As Gail pointed out,too much writing and not enough actual study. What climate scince needs is a professional legal body like engineers,geologists,lawyers,etc have.
As a quality assurance manager who was forced to introduce one of the ludicrous ISO programs,let me assure you that after a cost analysis of said implemantation and value added,it was scrapped pretty quickly.

“Principally, how representative is one reading at one point and a depth of the average temperature of the HUGE volume of water that it is being taken to represent. The uncertainty here is not millikelvin , it’s probably several degrees.”

I agree that this is the main problem.

The question is can this error be reduced by averaging across many measurements?

(The real calculation should use heat content, although we can get a rough idea of what this means with an “equivalent temperature” calculation. Just to try to understand principles we can think a bit about temperatures.)

The huge body of water that each float represents does in fact have a real average temperature. Each float will measure a temperature that deviates from this true average. That deviation is the error.

Some floats will find themselves warmer than the average for their region. Others will find themselves cooler than the average for their region. The error will be a random variable. For example, it may be approximately normally distributed, with a standard deviation of several Kelvin.

In this simple model the errors on the floats are uncorrelated: whether one float finds itself at a higher or lower temperature than the average for its region is independent of whether it’s neighbours are higher or lower than the average for their regions. Note, in this model it is the errors that are uncorrelated not the average. If a float in a high average region then it’s neighbour is more likely to be in a high average region. That’s a different question.

In that case then averaging, adding up these uncorrelated error terms, will indeed reduce their expected sum by a square root factor.

If you disagree with that, please explain where the disagreement is. Otherwise we can move on to clarify what changes in more realistic situations.

When I ride in an elevator, there is always an inspection sticker signed by the inspector.
When I stop at the gas pump, there are certification stickers certifying accuracy, who checked and when.
When I use the grocer’s scales, there are certification stickers certifying accuracy, who checked and when.

What I wonder is who has the responsibility for certifying the accuracy of Argo floats. I looked and was unable to find the specification for the thermometer component. I did find that Argo thinks of the floats as drop and run till dead.

I have a very hard time understanding that whatever temperature sensor they are using (thermocouple?) is consistently accurate for years without adjustment. About that adjustment; I did find this

“…It is important to understand the basic variable naming structure within the profile files. There are two versions of temperature, salinity and pressure in each file: a “real time” version (TEMP, PSAL, PRES) and a “delayed mode” version (TEMP_ADJUSTED, PSAL_ADJUSTED, PRES_ADJUSTED). It is recommended that users work with the delayed mode, or adjusted version, if it is filled.
In the “D” files, the adjusted variables are filled with the data that has been corrected after examination by the oceanographic experts, making it the highest quality data for that profile…”

“…Uncertainties less than 0.5oC are shaded in Fig. 5 to represent the achievable accuracy for upper layer
temperature estimation. This is equivalent to an accuracy in bimonthly heat content changes of 15 W/m2 for a 50 m thick layer. At that level of accuracy, errors in seasonal changes in heat content are comparable to the errors sought in air-sea heat exchange estimates. It should be noted that the temperature and heat storage errors can be reduced by temporal or spatial averaging or through combination of in situ data with altimetric data (see next section). Of the three terms in the oceanic heat balance – storage, air-sea flux, and ocean heat transport – the storage term is potentially the most accurate because it is not subject to large systematic errors. Large areas exist in the Pacific where the desired accuracy is not available from the present XBT network (Fig. 5). The 3o by 3o array attains 0.5oC accuracy over most of the domain….”

So, we do not know the specifications for the thermometer(s) used in Argo, their life cycle, or relative accuracy. Nor do we know dependability.

From what I read of the link Leif provided, I did not see where the author’s zeroed their temperature. That is, Did the authors use any other study to determine relative accuracy of temperatures between the different versions of Argo floats nor how to aggregate their temperatures without aggravating gross errors.

Yeah, I know the “D” files are adjusted and considered accurate… Sure and there also a certification of accuracy that allows one to calculate accuracy to .01% heat gain?

Between you, Gary Swift, Curiousgeorge and others (engineers aware of the impossibility of such precision), Tallbloke and Nic Lewis (James Annan’s evidence of mistakes in Levitus being stonewalled by Levitus and Science mag) I think we have sent the whole wretched shabang to Davey Jones, scuttled faster than any official peer-review could salvage.

The change in ocean heat content is dominated by changes in the top 300 meters or so. Yes, there is modest warming below 300 meters (how could there not be?), but most of the accumulation of heat is in fact relatively close to the surface. The increase in temperature in the top 300 meters is not the tiny number that the “average of 2000 meters” indicates. There is of course uncertainty in the measured ocean heat content (Argo is by no means perfect!), but the continuing trend over time suggests a gradual accumulation of heat.

Which is not at all surprising when you consider that the ocean surface temperature has increased modestly (about 0.6 – 0.7C) over the past 100 or so years. I have a sincere question for you: do you really doubt that a rising ocean surface temperature would not be expected to lead to a rising ocean heat content? I can understand arguing about uncertainty in the exact values; I can’t understand arguing that a significant increase in ocean heat content is not expected based on the historical ocean surface temperature trend.

ISO 9000 is like any other tool, capable of being used in foolish ways. I’ve been to companies that “have” SPC and proudly showed me walls wallpapered with computer printouts of control charts. But when I asked about various footprints I saw in the charts, I got blank looks on the bounceback. I had to tell them that SPC was not something you “have”, it’s something you “do.”
The same can be said for ISO 9000. It is certainly possible to turn it into a bureaucratic mess, especially if you approach it as “another paperwork requirement” rather than as an opportunity to study your processes systematically for inefficiencies, optimize those processes, then standardize and control to the optimum. The requirements of the standard are not especially onerous and can be found back in the Grand-daddy of em all, good ol’ MIL-Q-9858A.
+ + +
Precision, whether by the SQRT(n) or no, is a different critter from accuracy. It’s possible to get a very precise estimate of a totally inaccurate figure. Which is why “error bars” are not the whole story. There are other sorts of errors. My old boss, Ed Schrock, one of the founders of ASQC, liked to talk about “Errors of the Third Kind,” which was simply getting the wrong kind of data to begin with.
Besides, no matter how many men and women (n) you may measure, the tight precision on the average number of testicles will be utterly without physical meaning.
+ + +
It is always interesting to see confidence intervals on a parameter presented as if they were prediction intervals on the actual measurements. The former are always narrower than the latter; esp, if you start with five year rolling averages as your “data.”

i have not read all the above but speaking as a layperson nothing manmade continues to work the same after a period of time — particularily if it is around salt water. Do they take some of these out of the water and check to see if they are still accurately recording data? They must have some spot check program in place — but wait — this is government funded — maybe not. If such exists it would be nice if it were given a quick mention to allay needless doubts in an old boatboy’s mind..

The change in ocean heat content is dominated by changes in the top 300 meters or so. Yes, there is modest warming below 300 meters (how could there not be?), but most of the accumulation of heat is in fact relatively close to the surface. The increase in temperature in the top 300 meters is not the tiny number that the “average of 2000 meters” indicates. There is of course uncertainty in the measured ocean heat content (Argo is by no means perfect!), but the continuing trend over time suggests a gradual accumulation of heat.

Thanks, Steve. Dunno about “dominated”. According to the graphs in the paper under discussion, about half the warming has taken place below 300 metres, and half above 300 metres. Fifty-fifty doesn’t scream “dominated by” to me.

Regardless of that, this gives us a change in the top 300 metres of about 0.3°C. Not sure what your point is, that’s about a third of a degree change in a bit more than half a century.

Which is not at all surprising when you consider that the ocean surface temperature has increased modestly (about 0.6 – 0.7C) over the past 100 or so years. I have a sincere question for you: do you really doubt that a rising ocean surface temperature would not be expected to lead to a rising ocean heat content?

I fear we don’t know enough about the ocean temperature a hundred years ago to say how much it has warmed since then with any degree of accuracy.

Setting that aside, you ask if a rising ocean surface temperature would “lead to” a rise in oceanic heat content? No, it wouldn’t lead to a rise in OHC, they’d occur simultaneously. Change in temperature is a measure of change in heat content.

I can understand arguing about uncertainty in the exact values; I can’t understand arguing that a significant increase in ocean heat content is not expected based on the historical ocean surface temperature trend.

I haven’t noticed anyone arguing that an increase in ocean heat content is “not expected”, so it’s unclear what you are objecting to here.

He described the process of temperature measurement in those earlier times, as he and his colleagues had spent many years taking those temperatures:

“In the 1960s, more ships were out at sea: from Fisheries Laboratories, U.S.
Coast and Geodetic Survey (now NOAA), and research institutions at Scripps (La
Jolla, Calif.), Woods Hole (Massachusetts), Miami, and Texas A&M (in the Gulf of
Mexico). The British sailed the new Discovery, the Germans the new Meteor, and
there were small ships sailing from Denmark, Japan, and France. Many cruises
were dedicated to the geophysics of the sea floor, where deep-ocean casts for
water and temperatures were few and far between.”

Surface water samples were taken routinely, however, with buckets from the deck
and the ship’s engine-water intake valve. Most of the thermometers were
calibrated into 1/4-degrees Fahrenheit. They came from the U.S. Navy. Galvanized
iron buckets were preferred, mainly because they lasted longer than the wood and
canvas. But, they had the disadvantage of cooling quickly in the winds, so that
the temperature readings needed to be taken quickly.

I would guess that any bucket-temperature measurement that was closer to the actual temperature by better than 0.5° was an accident, or a good guess. But then, no one ever knew
whether or not it was good or bad. Everyone always considered whatever reading was made to be precise, and they still do today.

The archived data used by Levitus, and a plethora of other oceanographers, were taken by me, and a whole cadre of students, post-docs, and seagoing technicians around the world. Those of us who obtained the data, are not going to be snowed by the claims of the great precision of “historical data found stored in some musty archives.” ”

As Willis has shown, those claims of precision are still there.

Stevenson trained NASA astronauts in oceanography and marine meteorology. He was Secretary General of the International Association for the Physical Science of the Oceans from 1987
to 1995, and worked as an oceanographer for the U.S. Office of Naval Research for 20 years.

thermometer mounted in one location in the pool. Suppose we take one measurement per day. How long will we have to take daily measurements before we know the temperature of the entire pool full of water to the nearest two thousandths of a degree C?
———–
Interesting question.

Let’s change it slightly. Let’s measure temperature every 1 second with a precision of 0.1C.

Number of readings per day is 60x60x24.
That’s 86,400.
So 0.0003C is the precision for the average measurement assuming the pool is in equilibrium and isolated.

What we don’t know is how much variation there is in the pool due to changes in heating and cooling. Air currents and other stuff like clouds can affect this. Then you need to look at the measurements and their distribution and the frequency properties of the noise.

I’ve converted the graph of the 0-2000 metre ocean heat content shown in Figure 1 back into units of temperature. Figure 2 shows that result.
———–
I don’t know how it’s possible to do that. The heat capacity of water is not fixed. It varies with temperature and possibly even a little with pressure.

why didn’t the oceans warm in the slightest from about 1978 to 1990, while CO2 was rising and the surface temperature was increasing?
———
Changes in ocean circulation causing redistribution of the heat perhaps?. Since sea surface temps strong influence air surface temp this implies most of the discrepancy was at depth.

JK says:
>>
In this simple model the errors on the floats are uncorrelated: whether one float finds itself at a higher or lower temperature than the average for its region is independent of whether it’s neighbours are higher or lower than the average for their regions. Note, in this model it is the errors that are uncorrelated not the average. If a float in a high average region then it’s neighbour is more likely to be in a high average region. That’s a different question.

In that case then averaging, adding up these uncorrelated error terms, will indeed reduce their expected sum by a square root factor.

If you disagree with that, please explain where the disagreement is. Otherwise we can move on to clarify what changes in more realistic situations.
>>

Within the assumption that these errors are normally distributed and uncorrelated that seems correct. The question is what is the error of any reading , maybe this could be assumed to be less than 10K for example but I’m not sure how it could be evaluated.

Then there is : square root of what. the paper states that many cells have only one reading.

This version has the supplementary information on how they calculate the uncertainty due to propagation of errors in the averaging technique. You have to read it a few times but the crux is that they start with a complicated formula from another paper but do not have enough data to apply it , so they start doing some very inappropriate simplifications.
>>
… may be from one observation in data sparse regions up to several hundred or more.

Ideally, we would like to have a time series of measurements in each ODSQ [one degree sqr] with which we can produce statistics but this is simply not possible with the available data. Hence to evaluate standard deviations we will use the spatial variance of ODSQs containing data.
>>

For heavily populated squares they have a mean and a std error around that mean. Which, with lots of data, should be relatively small.
The problem is, for the cells with few data, they use the std error of the well populated cells and assume this reflects the error of single reading from the true mean.

Now if you stop to think, that means that they are incorrectly assuming the error of a one-off reading is the same as the error of a well balanced sample with hundreds of readings.

So their uncertainty calculations seem to be based on attributing the uncertainty for “several hundred” readings to cells of just ONE reading.

That dirty little secret gets tucked away in the S.I. which is not even available in the published version of the paper.

Now, until they can be bothered to do a correct analysis and a valid error estimation, using “hundreds” instead of one suggests that their error estimates are at least AN ORDER OF MAGNITUDE too small.

That is probably at least some way to Willis’ puzzle in the other thread:

To actually measure the oceans temperature, applying Shannons sampling theorum, it would be necessary to have enough thermometers to have twice the highest 3d fourier transform spatial frequency in the data. Given the numerous hot and cold oceanic currents, which would introduce relatively high spatial frequency components, this would suggest an impossible number. Dividing by the square root of the number of measurements is pointless in this situation. That would only reduce the gaussian noise of the individual measurements, which could be assumed to be fairly precise.

If high frequency components are ignored, then they fold back into the measured spectrum with approximately equal power to whatever power they have at the ignored frequencies, greatly reducing the low frequency measurement accuracy.

Let’s argue this from another angle. The oceans have warmed. Knowing the theorized mathematical equation for the ability of long wave radiation to warm the ocean skin, and thus by mixing, the layers below the mixing, it would be possible to determine what amount of that warming could be due to re-radiated LW infrared. It would also be possible to determine the part of THAT warming that is due to the anthropogenic increase in CO2.

My hypothesis would be that the LW warming would fall within the standard error of their data. This is a paper that would then appear to point towards a natural phenomenon.

Bonus question. Suppose we have an Olympic-sized swimming pool, and one perfectly accurate thermometer mounted in one location in the pool.

If it were an Argo bouy, it would be stuck at the outlet drain within a few minutes, because Argo bouys are free floating. In the ocean this means they drift towards areas of downwelling which are warmer and away from areas of upwelling which are cooler.

My question about the Argo floats has to do with the build up of bio material on the surface of the diving units. I suspect that there is something in place to control the film buildup, but from just using a squeege in my shower, I know that over time buildup still occurs. The film will affect the conductivity, and definitely with a change in conductivity, the measurement will drift. This would be true even if there weren’t currents etc. Moreover, the drift would be positive, as the electronics emit heat, small as that amount might be, it still would cause an upward bias. SInce the accuracy with which they are perporting to measure the temperature is so good, it would seem to be necessary to take into account small error contributions to the temperature measurement.

The above quibble is void if there is something like a plasma cleaner built into the devices.

The CAGW crowd is a part of a loose coalition of like-minded individuals that want to fundamentally remake the world in general and these United States in particular. Unfortunately (for them) the end results of their agenda are easy to see if you care to look.

According to the 1950 census, Capitalism and the auto industry had made Detroit one of the richest cities in the US and by extension the world. It is now number two. From the bottom. Ahead of only Cleveland.

The 1950 census also showed that Capitalism and the auto industry had created the largest, richest Black (as in African decent of ANY nationality) community in the world. Everything bad said about Henry Ford is true. He also put business ahead of most everything else, so all he cared about was how hard a man would work. He hired a lot of Americans who just coincidentally had African ancestry because they would work hard. (Imagine that: judging a man on the content of his character some half a century before it became a liberal cliché!) In 2010, the city council proposed bulldozing some forty (yes, 40) square miles of abandoned housing. The richest Black community in the world had been rendered uninhabitable.

Chicago, New York and California are headed the way of Detroit, Buffalo, and Flint.

Texas is holding out, but the current régime is using the EPA to shut down electric power production here. That would, of course, cripple the economy. The reason is so that the economic refugees fleeing Democrat party strongholds would have nowhere to go. (It is sort of like the reason that the Berlin Wall was built.)

My question about the Argo floats has to do with the build up of bio material on the surface of the diving units. I suspect that there is something in place to control the film buildup, but from just using a squeege in my shower, I know that over time buildup still occurs.

Interesting question. The Argo buoys float most of the time at 1,000 metres (0.6 miles) down in the ocean. At that depth, I doubt that there would be much buildup of anything, because there’s no sunlight to support it. The “photic zone” in the open ocean, where there is at least 1% of the surface sunlight, is generally taken as the area above 200 metres. So at 1000 metres, there’s no plant growth to build up on the floats.

This version has the supplementary information on how they calculate the uncertainty due to propagation of errors in the averaging technique. You have to read it a few times but the crux is that they start with a complicated formula from another paper but do not have enough data to apply it , so they start doing some very inappropriate simplifications.

… may be from one observation in data sparse regions up to several hundred or more.

Ideally, we would like to have a time series of measurements in each ODSQ [one degree sqr] with which we can produce statistics but this is simply not possible with the available data. Hence to evaluate standard deviations we will use the spatial variance of ODSQs containing data.

For heavily populated squares they have a mean and a std error around that mean. Which, with lots of data, should be relatively small.

The problem is, for the cells with few data, they use the std error of the well populated cells and assume this reflects the error of single reading from the true mean.

Now if you stop to think, that means that they are incorrectly assuming the error of a one-off reading is the same as the error of a well balanced sample with hundreds of readings.

So their uncertainty calculations seem to be based on attributing the uncertainty for “several hundred” readings to cells of just ONE reading.

Thanks for that reference, P. That lack of observations was my problem as well, particularly at depth. For some deeper depths, there is very little data. I find it difficult to conceive that you can get real numbers from no data …

The NCDF file of the World Ocean Atlas climatology is here (WARNING-570 Mb FILE!). It is divided into 1° gridcells and has 24 depth levels. It shows that some 42% of the gridcell/depth combinations have no data. Another 17% have only one observation for the given gridcell and depth, and 9% have two observations. In other words, the median number of observations is 1 …

It takes an absolute minimum of three observations to give us a standard error for the climatology. That indicates that only about a third of the locations (gridcell/depth) have enough data to even calculate an error …

Finally, I cannot find anywhere the data for the deeper calculations. The WOA climatology only goes down to 1500 metres depth …

All of which spells trouble in my world, but doesn’t seem to bother them …

mtobis, that is the fallacy that is being discussed. I am going to expand on what markx said.

IF you are taking 10 or 25 or 100 readings with the same instrument within a short time period of a UNIFORM material in a lab, then you can use the average to give you a very good estimate of the “True Value” with tight error bars (+/- 2 sigma.) Once you are talking about a non-uniform material (the ocean) measured by different instruments at different times at different depths at different locations then you are talking about huge error bars because you adding up all the errors inherent in each measurement and not increasing the accuracy by repeating the measurement under the same conditions.

Think of that swimming pool again vs a mix room tank filled with water and with specially engineered blender blades. I dump the same percentage of a chemical into the water of both the swimming pool and the mix tank (blenders on) a half hour later I take 100 samples from the mix tank and from the pool at different depths and at different locations. With the mix tank I use the same equipment and technician to analyse the 100 samples. With the swimming pool I use different people to take each sample at different depths and at different locations. I use different people at different labs with different equipment to analyse for the chemical.

Do you really think I am going to come up with the same statistical distribution for the two sets of data points and similar standard deviation and therefore similar error bars? Or do you think the swimming pool is going to have a much wider spread (range) in the data and therefore a much larger error?

Which mean of the two sets of data do you think is going to come closer to the “True Value,” that is the known percentage of the chemical placed in the water?

The swimming pool data is analogous to the ocean data and Levitus et al. are trying to convince us they are dealing with a mix tank with the blender on when they apply the statistics to estimate the error.

DR says: @ April 23, 2012 at 9:34 am
If there are any fellow Metrologists following, do you also split a gut laughing when seeing the claimed error bars for many of these so-called “studies”? In the real world, uncertainty must be accounted for empirically, not by playing statistics games.
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Yes, I ran a lab and I know how hard it is to get decent data under lab conditions much less field conditions. Trying to get good interlab correlation among the various plants had us tearing our hair out trying to find the sources of error. Temperatures good to .02 C from 1955 ocean measurements??? ROTFLMAO

We had this discussion at Boeing in the ’90′s…..
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VERY small world. In the 90’s I worked for a company that sold aircraft turbine blades to Boeing. I had a dust up with them when they refused to fire an obnoxious Lab tech that I finally nailed for falsifying data. (It was a bit of gorilla warfare for about two years) I am the one who got fired BTW because the lab tech had an “Angel” placed high up. So much for the usefulness of ISO or the Federal Aviation Administration. It took the loss of three planes to finally nail that company.

…. There is no way to separate the contributing wavelengths that vary anywhere from solar ultra violet to the far end of the infrared spectrum, so in this regard, the claim of a rising heat content as being a proof that greenhouse gases were the cause is patently ridiculous.
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Actually there is given this graph of the solar radiation intensity for different wavelengths at various ocean depths. The climate scientists are shooting themselves in the foot and proving it is the SUN not CO2 that is the culprit for ocean heating. This is because as the graph states there is no absorption of energy at depth from the wavelengths given off by GHGs. Those wavelengths are around 10 micrometers and well beyond where the chart approaches zero around a wavelength of 2.5 micrometer. ( depth of 0.01m) Essentially the GHG energy can not penetrate beyond the surface “skin”

In colder waters with less solar radiation results in small or no isothermal surface layer. The temperature continuously declines with depth from the surface…. Knowledge of the temperature profile and hence the sound speed profile, enables the prediction of sound transmission paths. Such information serves as input to the tactical environment in which submarine and surface navies operate…

Engineers have to get the science right. They can not play the games ivory tower scientists do or they fail.

stevefitzpatrick says:
April 23, 2012 at 7:06 pm
…Which is not at all surprising when you consider that the ocean surface temperature has increased modestly (about 0.6 – 0.7C) over the past 100 or so years. I have a sincere question for you: do you really doubt that a rising ocean surface temperature would not be expected to lead to a rising ocean heat content? I can understand arguing about uncertainty in the exact values; I can’t understand arguing that a significant increase in ocean heat content is not expected based on the historical ocean surface temperature trend.
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The problem is that when a “scientist” makes claims for impossible precision/accuracy in the measurements (a statistics/math mistake) it calls into doubt the entire body of data that he has adjusted and manipulated.

Do I think the oceans have warmed? Probably but I would be a lot less cynical if I did not see so much game playing going on.

ISO 9000 is like any other tool, capable of being used in foolish ways.
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As W. Edwards Deming said: “Quality starts in the boardroom.” It does not matter what system is used if $$$ is all that concerns the members of the board.

My other big gripe was Just in Time. One nasty ice storm and you are up the creek without a paddle, and have nothing to go into the furnaces. (Fought and lost that battle too until nature whapped the CEO upside the head)

Smokey says: @ April 24, 2012 at 7:06 am
America is a “can-do” country that can out compete anyone. But we are being sold out by anti-American traitors. There is no better term for what is being done.
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Bill Tuttle says:
April 24, 2012 at 1:16 pm
Actually, there are several — but there are ladies present…
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Don’t think us ladies haven’t thought those terms too but I prefer traitor because it is so accurate.

I have been traveling, and was not able to respond earlier. You said:
“No, it wouldn’t lead to a rise in OHC, they’d occur simultaneously. Change in temperature is a measure of change in heat content.”

That is not really correct. If the surface temperature of the ocean were to increase and then stay the same, there would be continuous accumulation of heat over at least hundred of years, and probably over ~1,000 years. The rate of down-mixing through the thermocline is extremely slow, especially past the first few hundred meters. The shape of the thermocline itself (near exponential temperature drop off below the surface layer) is exactly the expected shape for slow down-mixing combined with slow up-welling of abyssal water.

ARGO seems to me to be the best hope for constraining climate sensitivity; I honestly do not understand your many objections to ARGO data. The issue of “inadequate coverage” which you raise in multiple posts is not so strong an argument as you seem to suggest. The surface temperature does indeed vary quite a lot, both spatially and temporally, but below the surface at constant depth the temporal and spacial variability both decline a lot.

Consider the ARGO float cycle:
“A typical Argo float mission is to profile from 2000 m depth to the sea surface every 10 days. On deployment, the float sinks to a depth of 1000 m and drifts with the ocean currents for 9 days. Then the float sinks deeper to its profile depth (usually 2000 m) before starting to ascend through the water column measuring temperature, salinity and pressure as it rises. Once at the surface it transmits location and profile data via satellite to land-based Argo data centres. After transmission the float sinks again and repeats the cycle.”
The floats migrate over quite large distances, not at the surface, but at a depth of 1000 meters, which shows that there is considerable horizontal (more accurately, isopycnal) velocity even at considerable depth. The point of which is that this horizontal motion makes the ocean remarkably more uniform in temperature profile with depth than might be indicated by examining variation in near-surface temperature. The requirement of sampling frequency and spacial coverage to generate a very reasonable estimate of total heat content at depth is less that at first meets the eye.

A lot of people (including some who are quite skeptical of the likelihood of extreme future warming) appear to agree on the relatively good quality of the ARGO data. According to Craig Loehle last year: “The quality of the Argo data is evident in that the annual cycle with a period exactly 365 days (see my paper cited) is evident in this data”.

The key thing is that ARGO was specifically designed to generate a credible estimate of changes in ocean heat content over annual and longer time scales. The fact that many climate scientists have publicly questioned the accuracy of ARGO data (or at least ignored the ARGO data) when that data conflicted with projections of rapid heat accumulation suggests to me that the system is probably reasonably close to correct, and probably a lot more accurate that you give it credit for. The story ARGO is trying to tell us is that climate sensitivity is far lower than CGCM’s suggest. It is a story I am inclinded to believe.

“No, it wouldn’t lead to a rise in OHC, they’d occur simultaneously. Change in temperature is a measure of change in heat content.”

That is not really correct. If the surface temperature of the ocean were to increase and then stay the same, there would be continuous accumulation of heat over at least hundred of years, and probably over ~1,000 years. The rate of down-mixing through the thermocline is extremely slow, especially past the first few hundred meters. The shape of the thermocline itself (near exponential temperature drop off below the surface layer) is exactly the expected shape for slow down-mixing combined with slow up-welling of abyssal water.

Steve, that’s exactly my point. Wherever the temperature is increasing, whether at the surface or at depth, the heat content is commensurately increasing. They are interchangeable measurements of the same thing, and are directly convertible from one unit (°C) to the other (J).

ARGO seems to me to be the best hope for constraining climate sensitivity; I honestly do not understand your many objections to ARGO data. The issue of “inadequate coverage” which you raise in multiple posts is not so strong an argument as you seem to suggest. The surface temperature does indeed vary quite a lot, both spatially and temporally, but below the surface at constant depth the temporal and spacial variability both decline a lot.

If you think that is true, you’ll have to demonstrate it with numbers, because I have demonstrated the opposite numerically in Decimals of Precision. You can’t just say you don’t think it’s true. If you don’t, you’ll have to come up with the math to show me where my numbers are wrong.

Look, I love the Argo data, it’s among the best we have, and I have lauded it repeatedly. My problem is not the data, it’s the claims that some scientists have made using the data, claims that don’t match reality.

Willis,
You said earlier: “Setting that aside, you ask if a rising ocean surface temperature would “lead to” a rise in oceanic heat content? No, it wouldn’t lead to a rise in OHC, they’d occur simultaneously”
It seems to me you are arguing about semantics. I am quite aware of how temperature change and heat content are related. OK, but the substantive point remains; changes in surface temperature do not directly reflect the change in heat content below the surface, and a change in surface temperature takes centuries to fully influence the total ocean heat content. The measured surface temperature could be constant for a very long time, and the total ocean heat content could be changing significantly, either up or down. Do you not agree this is true?

With regard to showing that there is much less spacial and temporal variation below the surface layer: I will need to do some digging. I remember seeing convincing data, but I will be traveling for a few more days so can’t search now.

Willis,
You said earlier: “Setting that aside, you ask if a rising ocean surface temperature would “lead to” a rise in oceanic heat content? No, it wouldn’t lead to a rise in OHC, they’d occur simultaneously” It seems to me you are arguing about semantics. I am quite aware of how temperature change and heat content are related. OK, but the substantive point remains; changes in surface temperature do not directly reflect the change in heat content below the surface, and a change in surface temperature takes centuries to fully influence the total ocean heat content.

I don’t see anyone who is claiming that we can tell the OHC from the surface temperature, that’s why the temperature is sampled at 24 different depths from the surface down to 1500 metres … so I’m not clear who you are arguing against.

Nor do I see anyone saying that the time constant of the ocean is other than long, centuries long.

So I’m not sure who you think you are arguing against … but it ain’t me, and I don’t think it’s anyone here …

Willis writes “each year’s value is actually a centered five-year average … which makes me nervous already, very nervous. Why not show the actual annual data? What are the averages hiding?”

It would be nice to know their precise algorithm for calculating the result. Then one can ask how much data must one drop for the result to fall outside their error bars? The answer to that would, I feel, be telling of the robustness of the result.

… With regard to showing that there is much less spacial and temporal variation below the surface layer: I will need to do some digging. I remember seeing convincing data, but I will be traveling for a few more days so can’t search now.

Thanks, Steve. If you look at the standard error of the mean you can see which areas have variations and which are more smooth. Certainly things are smoother at say 500 metres than at the surface … but they are far from even.

Note that even in a single month we have variations greater than half a degree at a depth of 500 metres … sure, it’s less than at the surface as you’d expect, but it is hardly smooth. Not only that, but it occurs in some parts of the ocean and not others, which is not what I had expected …

Gail Combes sez “Once you are talking about a non-uniform material (the ocean) measured by different instruments at different times at different depths at different locations then you are talking about huge error bars because you adding up all the errors inherent in each measurement and not increasing the accuracy by repeating the measurement under the same conditions.”
Indeed. At the ‘precision’ of .001°, there is no such thing as a right answer, as the hypothetical point which is being ‘measured’ is changing too fast.

BTW, Gail, though you are a possibly hairy primate, I suspect it was guerrilla war you were waging.

Willis,
Thanks for finding that data. The areas were the variability at depth is the greatest are the eastern coast of Japan and the Gulf Stream, both regions are subject to strong horizontal shear due to the velocity of the surface current. No doubt that does cause locally exaggerated eddy mixing and higher variability. I had not seen that data before.

I would bet they are doing things like averaging measurements and assuming they are uncorrelated, so that they can scale the uncertainties by the inverse square root of the number of measurements. And, that assumption is, of course, bollocks. Inappropriate statistical manipulations have driven the CO2 bandwagon from the very start.